Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received July 19, 2013; final manuscript received October 27, 2013; accepted manuscript posted November 27, 2013; published online February 5, 2014. Editor: Beth Winkelstein.

Abstract

Cartilage fissures, surface fibrillation, and delamination represent early signs of hip osteoarthritis (OA). This damage may be caused by elevated first principal (most tensile) strain and maximum shear stress. The objectives of this study were to use a population of validated finite element (FE) models of normal human hips to evaluate the required mesh for converged predictions of cartilage tensile strain and shear stress, to assess the sensitivity to cartilage constitutive assumptions, and to determine the patterns of transchondral stress and strain that occur during activities of daily living. Five specimen-specific FE models were evaluated using three constitutive models for articular cartilage: quasilinear neo-Hookean, nonlinear Veronda Westmann, and tension-compression nonlinear ellipsoidal fiber distribution (EFD). Transchondral predictions of maximum shear stress and first principal strain were determined. Mesh convergence analysis demonstrated that five trilinear elements were adequate through the depth of the cartilage for precise predictions. The EFD model had the stiffest response with increasing strains, predicting the largest peak stresses and smallest peak strains. Conversely, the neo-Hookean model predicted the smallest peak stresses and largest peak strains. Models with neo-Hookean cartilage predicted smaller transchondral gradients of maximum shear stress than those with Veronda Westmann and EFD models. For FE models with EFD cartilage, the anterolateral region of the acetabulum had larger peak maximum shear stress and first principal strain than all other anatomical regions, consistent with observations of cartilage damage in disease. Results demonstrate that tension-compression nonlinearity of a continuous fiber distribution exhibiting strain induced anisotropy incorporates important features that have large effects on predictions of transchondral stress and strain. This population of normal hips provides baseline data for future comparisons to pathomorphologic hips. This approach can be used to evaluate these and other mechanical variables in the human hip and their potential role in the pathogenesis of osteoarthritis (OA).

Figures

Representative FE model and mesh convergence analysis. (a) View of the whole joint. The red box indicates the region shown in the remaining images. Lines in the remaining images show discretization. (b) FE model with three elements through the cartilage thickness. (c) FE model with four elements through the cartilage thickness. (d) FE model with five elements through the cartilage thickness (this was the converged mesh density). (e) FE model with six elements through the cartilage thickness.

Uniaxial stress response of the three constitutive models. Experimental data are shown. At small strains (stretch values near 1.0), there were minimal differences between the three models. At larger tensile strains, there were drastic differences. The EFD model was the stiffest at higher levels of stretch due to the fiber contribution to the response, likely resulting in both the higher τmax and lower E1 at large magnitudes (Fig. 5). In compression (stretch values less than 1), the EFD and VW constitutive models predicted nearly identical responses. Error bars = standard deviation.

E1 and τmax results on the acetabulum in the EFD models of one specimen. (a) Lateral view of the acetabulum with the six anatomic regions used for analysis. (b) E1 at the articular surface. (c) τmax at the osteochondral interface.

Results in six anatomical regions on the acetabular cartilage. (a) Peak τmax at the osteochondral interface. (b) Average τmax at the osteochondral interface. (c) Peak E1 at the articular surface. (d) Average E1 at the articular surface. At high stress values, the EFD models predicted the largest stresses. A high strain values, the neo-Hookean models predicted the largest strains. Error bars = standard deviation.

Results through the depth of the femoral cartilage during AH. (a) τmax at the location of the osteochondral peak. (b) E1 at the location of the articular peak. While τmax near the osteochondral interface was larger in the EFD model, it was larger in the neo-Hookean (nH) models near the articular surface. For all constitutive models, E1 peaked just below the articular surface. * indicates differences between EFD and VW, ‡ indicates differences between EFD and nH, and § indicates differences between VW and nH. Error bars = standard deviation.

Cut planes for femoral E1 as reported in Fig. 6(b). Each column is for one specimen. The top row indicates the location of the cut planes. The next three rows are the nH, VW, and EFD model results, respectively. The arrows in each cut figure indicate the location and direction of sampling.

E1 and τmax in six anatomical regions on the acetabulum the EFD models. (a) Peak τmax at the osteochondral interface. (b) Average τmax at the osteochondral interface. (c) Peak E1 at the articular surface. (d) Average E1 at the articular surface. ‡ indicates p ≤ 0.05 against all other regions. † indicates p ≤ 0.05 against all other regions except the one with the same symbol in the same panel. * indicates p ≤ 0.05 against the listed region. Error bars = standard deviation. There were distinct regional differences in E1 and τmax, with the largest values occurring the AL region and the smallest values occurring in the PM region.

τmax in the normal subject model without the labrum compared to the normal subject model with the labrum. (a) Acetabular τmax results at the articular surface, at the osteochondral interface and transchondrally at the location of the osteochondral cartilage peak. Note that the location of the osteochondral peak is identical in the models with and without the labrum. (b) Transchondral τmax for the both the acetabular and femoral cartilage in the model without the labrum (“cartilage”) and the model with the labrum (“both”). While the acetabular labrum decreased the magnitudes of τmax, articular, osteochondral, and transchondral τmax patterns were relatively unaffected. The acetabular labrum had a similar effect on predicted E1.

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